When a string is divided into three segments of lengths \(l_1\), \(l_2\) and \(l_3\), the fundamental frequencies of these three segments are \(\nu_1\), \(\nu_2\) and \(\nu_3\) respectively. The original fundamental frequency (\(\nu\)) of the string is:

A \(200~\text{W}\) sodium street lamp emits yellow light of wavelength \(0.6~\mu\text{m}.\)$$ Assuming it to be \(25\%\) efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is:
1. \(1.5\times 10^{20}\)
2. \(6\times 10^{18}\)
3. \(62\times 10^{20}\)
4. \(3\times 10^{19}\)

Two ideal diodes are connected to a battery as shown in the circuit. The current supplied by the battery is:

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:

An electric dipole of moment \(p\) is placed in an electric field of intensity \(E.\) The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ}\)$$, the torque and the potential energy of the dipole will respectively be:
1. \(pE\text{sin}\theta, ~-pE\text{cos}\theta\)
2. \(pE\text{sin}\theta, ~-2pE\text{cos}\theta\)
3. \(pE\text{sin}\theta, ~2pE\text{cos}\theta\)
4. \(pE\text{cos}\theta, ~-pE\text{sin}\theta\)

In a CE transistor amplifier, the audio signal voltage across the resistance of 2 k$\Omega$ is 2V. If the base resistance is 1 k$\Omega$ and the current amplification of the transistor is 100, the input signal voltage is:

1. 0.1 V

2. 1.0 V

3. 1 mV

4. 10 mV

A coil of resistance \(400~\Omega\) is placed in a magnetic field. The magnetic flux \(\phi~\text{(Wb)}\) linked with the coil varies with time \(t~\text{(s)}\) as \(\phi=50t^{2}+4.\) The current in the coil at \(t=2~\text{s}\) is:$$

If the nuclear radius of \(^{27}\text{Al}\) is \(3.6\) Fermi, the approximate nuclear radius of \(^{64}\text{Cu}\) in Fermi is:
1. \(2.4\)
2. \(1.2\)
3. \(4.8\)
4. \(3.6\)